Answer
The axis of symmetry is $x=3$.
domain: $(-\infty 2\infty)$
range: $[$2, $\infty)$
Work Step by Step
To graph $f(x)=a(x-h)^{2}+k$,
1. Determine whether the parabola opens upward or downward.
If $a>0$, it opens upward. If $a<0$, it opens downward.
2. Determine the vertex of the parabola. The vertex is $(h, k)$.
3. Find any x-intercepts by solving $f(x)=0$.
The function's real zeros are the x-intercepts.
4. Find the y-intercept by computing $f(0)$.
5. Plot the intercepts, the vertex, and additional points as necessary
Connect these points with a smooth curve that is shaped like a bowl or an inverted bowl.
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$f(x)=(x-3)^{2}+2$
1. opens up (a=1).
2. vertex: (3, 2)$. $The axis of symmetry is $x=3$.
3. x-intercepts:
$0=(x-3)^{2}+2$
$(x-3)^{2}=-2$
(a square of a real number can not be -2)
No x-intercepts.
4. y-intercept:
$f(0)=(0-3)^{2}+2=11$
5. see graph
The axis of symmetry is $x=3$.
domain: $(-\infty ,\infty)$
range: $[$2, $\infty)$
